An Application

Now you will apply these steps to sketch wave functions for electrons in an electron microscope. Electron microscopes come in two basic varieties. The electrons in a scanning electron microscope strike a sample and interact with the electrons of the atoms on the surface of the sample. By observing the results of these interactions an image is created. In a transmission electron microscope, the sample is made very thin, so that the electrons pass through it. These electrons are picked up by a detector on the other side, and carry information about the material of the sample. We will consider the latter type here (See below).

 

 

In this example the microscope gives the electrons a total energy of 3eV. They are approaching a sample in which the potential energy due to repulsion from other electrons is 1eV.

 

Draw the potential energy diagram of the electrons indicating the potential and total energies inside the sample as well as in the empty space on either side.

 

Use the Wave Function sketcher and the steps you have studied to create the wave functions for the electrons in each region. Sketch or print your result. (Be sure to indicate the location of the boundaries on your sketch.)

 

Sketch the probability density and write a short interpretation.

 

If the sample is 10 nm thick, how many wavelengths of the electron wave will have to pass through the sample, before the electron emerges on the other side?